Problem: Simplify the following expression: $ p = \dfrac{q - 2}{-6q} - \dfrac{-3}{7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{q - 2}{-6q} \times \dfrac{7}{7} = \dfrac{7q - 14}{-42q} $ Multiply the second expression by $\dfrac{-6q}{-6q}$ $ \dfrac{-3}{7} \times \dfrac{-6q}{-6q} = \dfrac{18q}{-42q} $ Therefore $ p = \dfrac{7q - 14}{-42q} - \dfrac{18q}{-42q} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{7q - 14 - 18q }{-42q} $ Distribute the negative sign: $p = \dfrac{7q - 14 - 18q}{-42q}$ $p = \dfrac{-11q - 14}{-42q}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{11q + 14}{42q}$